Fundamental Operator-Functions of Degenerate Differential and Difference-Differential Operators in Banach Spaces Which Have a Noether Operator in the Principal Part

Abstract

Continuing the study by the first author, we construct fundamental operator-functions for some classes of degenerate differential operators (both ordinary and partial) and difference-differential operators in Banach spaces which have a Noether operator at the leading (time) derivative. To this end, we use the method of Jordan chains of Noether operators and the methods of distribution theory in Banach spaces.